General Inner Approximation of Vector-valued Functions

Abstract : This paper addresses the problem of evaluating a subset of the range of a vector-valued function. It is based on a work by Goldsztejn and Jaulin which provides methods based on interval analysis to address this problem when the dimension of the domain and co-domain of the function are equal. This paper extends this result to vector-valued functions with domain and co-domain of different dimensions. This extension requires the knowledge of the rank of the Jacobian function on the whole domain. This leads to the sub-problem of extracting an interval sub-matrix of maximum rank from a given interval matrix. Three different techniques leading to approximate solutions of this extraction are proposed and compared.
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Olivier Mullier, Eric Goubault, Michel Kieffer, Sylvie Putot. General Inner Approximation of Vector-valued Functions. Reliable Computing, Springer Verlag, 2013, 18, pp.117-143. ⟨hal-00935773⟩

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